Is Dynamic shutter speed in Sampled Motion Blur possible?
Since this property cannot be animated or driven, the only thing left is to control it with script:

import bpy
import math

def function(frame):
    # modify this function if you want
    return math.pow(4.75, (frame-30)/50) - 0.75

def my_handler(scene):
    # this code will be run on every frame change
    scene.render.motion_blur_shutter = function(scene.frame_current)

bpy.app.handlers.frame_change_pre.append(my_handler)


Run this in the Text editor, render the animation normally.
If you want to make changes after you ran the code, remove the handler first with typing this into the console: bpy.app.handlers.frame_change_pre.clear()

If you would like to animate the value, create a custom ID property for the scene which you can animate (name the property "shutter"):



And use this code (it copies the value into the shutter speed):

import bpy

def my_handler(scene):
    scene.render.motion_blur_shutter = scene["shutter"]

bpy.app.handlers.frame_change_pre.append(my_handler)